Weighted Mean

Weighted Mean: how to approach it

A weighted mean is an average where some values count more than others. Instead of treating every value equally, you multiply each value by its weight, add those products, then divide by the total of the weights.

Method

1. List the values and weights clearly.
2. Multiply each value by its weight.
3. Add all the weighted products.
4. Add all the weights.
5. Divide the total weighted sum by the total weight.

In symbols, if the values are (x_1, x_2, \dots) with weights (w_1, w_2, \dots), then [ \text{weighted mean} = \frac{\sum x_i w_i}{\sum w_i}. ]

Important details

• A larger weight means that value influences the mean more.
• Keep the weights in the denominator; do not average the values first.
• If the final result can be simplified, write it in simplest form.

Quick check

Your answer should lie between the smallest and largest values when all weights are positive. Also, recheck that the numerator is the sum of products, not just the sum of the values.